Analytic expression of the temperature increment in a spin transfer torque nanopillar structure

摘要

The temperature increment due to the Joule heating in a nanopillar spintransfer torque system is investigated. We obtain a time dependent analyticsolution of the heat conduction equation in nanopillar geometry by using theGreen's function method after some simplifications of the problem. While Holm'sequation is applicable only to steady states in metallic systems, our solutiondescribes the time dependence and is also applicable to a nanopillar-shapedmagnetic tunneling junction with an insulator barrier layer. The validity ofthe analytic solution is confirmed by numerical finite element methodsimulations and by the comparison with Holm's equation.